Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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          <pb o="277" file="0293" n="293" rhead="LIBER SECVNDVS."/>
          <p style="it">
            <s xml:id="echoid-s18796" xml:space="preserve">QVONIAM verò, vt in præcedenti propoſ. </s>
            <s xml:id="echoid-s18797" xml:space="preserve">oſtendimus, circuli horarum à meridie, vel media
              <lb/>
              <note position="right" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">Arcus ſignorũ
                <lb/>
              in horologio ę-
                <lb/>
              quinoctiali di-
                <lb/>
              uiduntur à li-
                <lb/>
              neis horarum à
                <lb/>
              mer. vel med.
                <lb/>
              noc. in partes
                <lb/>
              equales.</note>
            nocte diuidunt circulum quemcunque ex centro E, deſcriptum (eadem enim demonſtratio in omnem cir-
              <lb/>
            culum, quæ in circulum A C B D, ibi deſcriptum, conuenit) in partes æquales, fit vt in æquinoctiali ho-
              <lb/>
            rologio lineæ earundem horarum ſecent parallelos ſignorum in partes æquales, quippe qui circuli ſint ex
              <lb/>
            eodem centro E, deſcripti, vt in hac propoſ. </s>
            <s xml:id="echoid-s18798" xml:space="preserve">probatum eſt. </s>
            <s xml:id="echoid-s18799" xml:space="preserve">Id quod in nullo alio horologio contingit.
              <lb/>
            </s>
            <s xml:id="echoid-s18800" xml:space="preserve">Inęqualia enim ſpatia intercipiunt lineæ horarum à meridie, vel media nocte in parallelis ſignorum in
              <lb/>
            alijs horologijs deſcriptis.</s>
            <s xml:id="echoid-s18801" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div964" type="section" level="1" n="235">
          <head xml:id="echoid-head242" xml:space="preserve">PROBLEMA 51. PROPOSITIO 51.</head>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s18802" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem æquinoctiali
              <lb/>
            horologio deſcribere.</s>
            <s xml:id="echoid-s18803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18804" xml:space="preserve">SI loco parallelorum per ſignorum principia ductorum accipiantur paralleli arcuum diurno
              <lb/>
              <note position="right" xlink:label="note-0293-03" xlink:href="note-0293-03a" xml:space="preserve">Deſcriptio ar-
                <lb/>
              cuum ſignorũ
                <lb/>
              in eodem horo
                <lb/>
              logio æquino-
                <lb/>
              ctiali.</note>
            rum, & </s>
            <s xml:id="echoid-s18805" xml:space="preserve">pro radijs ſignorum radij arcuum diurnorum, deſcribentur in horologio æquinoctiali
              <lb/>
            paralleli arcuum diurnorum, quemadmodum parallelos ſignorum in præcedenti propoſ. </s>
            <s xml:id="echoid-s18806" xml:space="preserve">deſcri-
              <lb/>
            pſimus. </s>
            <s xml:id="echoid-s18807" xml:space="preserve">Quamobrem parallelos arcuum diurnorum in eodem æquinoctiali horologio deſcri-
              <lb/>
            pſimus. </s>
            <s xml:id="echoid-s18808" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s18809" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div966" type="section" level="1" n="236">
          <head xml:id="echoid-head243" xml:space="preserve">PROBLEMA 52. PROPOSITIO 52.</head>
          <p>
            <s xml:id="echoid-s18810" xml:space="preserve">CIRCVLOS Verticales in horologio codem æquinoctiali
              <lb/>
            delineare.</s>
            <s xml:id="echoid-s18811" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18812" xml:space="preserve">IN figura prima propoſ. </s>
            <s xml:id="echoid-s18813" xml:space="preserve">26. </s>
            <s xml:id="echoid-s18814" xml:space="preserve">huius libri notentur puncta n, & </s>
            <s xml:id="echoid-s18815" xml:space="preserve">o, vbi diameter Verticalis A C,
              <lb/>
              <note position="right" xlink:label="note-0293-05" xlink:href="note-0293-05a" xml:space="preserve">Verticales circu
                <lb/>
              li in codem ho
                <lb/>
              rologio quomo
                <lb/>
              do deſcribãtur.</note>
            parallelas per a, & </s>
            <s xml:id="echoid-s18816" xml:space="preserve">e, ductas ſecat; </s>
            <s xml:id="echoid-s18817" xml:space="preserve">& </s>
            <s xml:id="echoid-s18818" xml:space="preserve">recta a n, vel e o, transferatur in lineam meridianam ex loco
              <lb/>
            ſtyli, deorſum quidem in ſuperiori horologio, ſurſum autem in inferiori, vſque ad p. </s>
            <s xml:id="echoid-s18819" xml:space="preserve">Erit punctũ
              <lb/>
            p, Verticale, in quod nimirum cadit axis Horizontis, cum A C, axis Horizontis, ſeu diameter Ver-
              <lb/>
              <note position="left" xlink:label="note-0293-06" xlink:href="note-0293-06a" xml:space="preserve">30</note>
            ticalis, ſecet planum horologij vtriuſque per parallelas a n, e o, ductum in punctis n, & </s>
            <s xml:id="echoid-s18820" xml:space="preserve">o, infra
              <lb/>
            quidem locum ſtyli E, in ſuperiori horologio, ſupra verò in inferiori. </s>
            <s xml:id="echoid-s18821" xml:space="preserve">Quia verò recta a n, rectæ
              <lb/>
            e o, æqualis eſt, (Nam quia in triangulis E a n, E e o, anguli ad a, & </s>
            <s xml:id="echoid-s18822" xml:space="preserve">e, recti ſunt, & </s>
            <s xml:id="echoid-s18823" xml:space="preserve">anguli ad E, ver
              <lb/>
              <note position="right" xlink:label="note-0293-07" xlink:href="note-0293-07a" xml:space="preserve">15. primi.</note>
            ticem æquales, atque latera E a, E e, æqualia; </s>
            <s xml:id="echoid-s18824" xml:space="preserve">erunt etiam latera a n, e o, æqualia) idcircò iuſſimus
              <lb/>
              <note position="right" xlink:label="note-0293-08" xlink:href="note-0293-08a" xml:space="preserve">16. primi.</note>
            candem a n, vel e o, transferri in vtroque horologio in lineam meridianam infra vel ſupra lo-
              <lb/>
            cum ſtyli.</s>
            <s xml:id="echoid-s18825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18826" xml:space="preserve">HOC autem punctum Verticale p, comperiemus hac etiam induſtria. </s>
            <s xml:id="echoid-s18827" xml:space="preserve">Ex E, loco ſtyli duca-
              <lb/>
            tur ad meridianam lineam perpendicularis E F, ſtylo æqualis, & </s>
            <s xml:id="echoid-s18828" xml:space="preserve">ad punctum F, couſtituatur angu
              <lb/>
            lus E F p, complemento altitudinis poli æqualis, ita vt recta F p, ſecet lineam meridianam in pun
              <lb/>
            cto p; </s>
            <s xml:id="echoid-s18829" xml:space="preserve">infra quidem locum ſtyli in horologio ſuperiori, ſupra vero in inferiori. </s>
            <s xml:id="echoid-s18830" xml:space="preserve">Dico p, eſſe pun-
              <lb/>
              <note position="left" xlink:label="note-0293-09" xlink:href="note-0293-09a" xml:space="preserve">40</note>
            ctum Verticale. </s>
            <s xml:id="echoid-s18831" xml:space="preserve">Intelligatur enim triangulum E F p, conuerti circa rectam E p, donec rectum ſit
              <lb/>
            ad planum horologij, ac proinde in plano Meridiani exiſtat, punctumq́ue F, cum vertice ſtyli,
              <lb/>
            centrove mundi coniungatur, & </s>
            <s xml:id="echoid-s18832" xml:space="preserve">recta ipía E F, cum ſtylo, ſeu axe mundano. </s>
            <s xml:id="echoid-s18833" xml:space="preserve">Tranſibit Verticalis
              <lb/>
            circulus propriè dictus per verticem ſtyli, mundive centrum F, ac proinde per rectam F p, propte-
              <lb/>
            rea quòd Verticalis circulus cum axe mundi in Meridiani plano facit angulum complemento al-
              <lb/>
            titudinis poli æqualem, qualis eſt E F p, & </s>
            <s xml:id="echoid-s18834" xml:space="preserve">cum linea meridiana in Æquatore angulum altitudi-
              <lb/>
            ni poli ęqualem, vt conſtat; </s>
            <s xml:id="echoid-s18835" xml:space="preserve">qui quidem æqualis eſt illi angulo, quem idem Verticalis cum linea
              <lb/>
            meridiana plani horologij Aequatori æquidiſtantis conficit, qualis eſt angulus E p F. </s>
            <s xml:id="echoid-s18836" xml:space="preserve">Cum enim
              <lb/>
            ſectiones Meridiani, quas cum Aequatore, & </s>
            <s xml:id="echoid-s18837" xml:space="preserve">plano horologij illi parallelo facit, ſint parallelæ, fa-
              <lb/>
              <note position="right" xlink:label="note-0293-10" xlink:href="note-0293-10a" xml:space="preserve">16. vndec.</note>
            ciet communis ſectio Verticalis, & </s>
            <s xml:id="echoid-s18838" xml:space="preserve">Meridiani angulos æquales cum dictis lineis Meridianis, ex-
              <lb/>
              <note position="right" xlink:label="note-0293-11" xlink:href="note-0293-11a" xml:space="preserve">29. primi.</note>
              <note position="left" xlink:label="note-0293-12" xlink:href="note-0293-12a" xml:space="preserve">50</note>
            ternum videlicet, & </s>
            <s xml:id="echoid-s18839" xml:space="preserve">internum. </s>
            <s xml:id="echoid-s18840" xml:space="preserve">Quamobrem Verticalis propriè dictus planum horologii ſe-
              <lb/>
            cabit in p.</s>
            <s xml:id="echoid-s18841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18842" xml:space="preserve">POST hæc ducta recta F m, quæ faciat angulum E F m, altitudini poli æqualem, ita vt ſe-
              <lb/>
            cet meridianam lineam in m, puncto, per quod oſtendimus prope finem propoſ. </s>
            <s xml:id="echoid-s18843" xml:space="preserve">50. </s>
            <s xml:id="echoid-s18844" xml:space="preserve">huius libri
              <lb/>
            lineam horizontalem eſſe ducendam, ſumatur in linea meridiana ipſi F m, æqualis m e, ſiue infra
              <lb/>
            lineam horizontalem, ſiue ſupra. </s>
            <s xml:id="echoid-s18845" xml:space="preserve">Ex e, autem centro deſcripto circulo cuiuſcunque magnitudi-
              <lb/>
            nis, eoq́ue in gradus 360. </s>
            <s xml:id="echoid-s18846" xml:space="preserve">diſtributo, vel in partes pauciores, habita ratione magnitudinis horolo-
              <lb/>
            gij, (Nos eum diſtribuimus in 24. </s>
            <s xml:id="echoid-s18847" xml:space="preserve">vt ſingulæ grad. </s>
            <s xml:id="echoid-s18848" xml:space="preserve">15. </s>
            <s xml:id="echoid-s18849" xml:space="preserve">contineant) ducantur per puncta diuiſio-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s18850" xml:space="preserve">per centrum e, rectæ occultæ ſecantes lineam horizontalem in punctis, per quæ, & </s>
            <s xml:id="echoid-s18851" xml:space="preserve">punctũ
              <lb/>
            Verticale p, rectæ emiſſæ dabunt circulos Verticales, id eſt, communes ſectiones plani horologij,
              <lb/>
            & </s>
            <s xml:id="echoid-s18852" xml:space="preserve">circulorum Verticalium, quarum initium in vtroque horologio ſumitur à Verticali linea, </s>
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